a golf ball is hit with an initial speed of 35 m/s at an angle less than 45 degress above the horizontial (a) the horizontial velocity componant is (1)greater than (2)equal to or (3) less than the vertical velocity componant. Why? (b)If the ball is hit at an angle of 37 degress , what is the initial horizontial and vertical velocity componants?
(a) The initial vertical component is 35 sin theta and the initial horizontal component is 35 cos theta. The ratio is tan theta. Is this greater than or less than 1 when theta is less than 45 degrees? You figure it out.
(b)The formulas you need are provided above.
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(a) To determine whether the horizontal velocity component is greater than, equal to, or less than the vertical velocity component, we need to consider the nature of projectile motion.
Projectile motion can be broken down into two independent components: horizontal and vertical. The horizontal motion is constant without any acceleration, while the vertical motion is affected by gravity.
The initial velocity given (35 m/s) has two components: the horizontal component (Vx) and the vertical component (Vy). The angle given is less than 45 degrees, which means that the vertical component is greater than the horizontal component.
To find the answer to part (a), we simply need to compare the vertical and horizontal components of the velocity:
Vertical velocity component (Vy) = initial speed * sin(angle)
Horizontal velocity component (Vx) = initial speed * cos(angle)
Since the given angle is less than 45 degrees, sin(angle) will be greater than cos(angle), which means that the vertical velocity component (Vy) will be greater than the horizontal velocity component (Vx).
Therefore, the answer to part (a) is (1) greater than.
(b) To find the initial horizontal and vertical velocity components when the ball is hit at an angle of 37 degrees, we can use the same formulas mentioned above:
Initial horizontal velocity component (Vx) = initial speed * cos(angle)
Initial vertical velocity component (Vy) = initial speed * sin(angle)
Given:
Initial speed = 35 m/s
Angle = 37 degrees
Plugging in the values, we find:
Vx = 35 m/s * cos(37 degrees)
Vy = 35 m/s * sin(37 degrees)
Using a calculator or trigonometric table, we can calculate these values. The horizontal velocity component and vertical velocity component for an initial angle of 37 degrees will be specific numerical values based on the calculations mentioned above.